共查询到20条相似文献,搜索用时 15 毫秒
1.
《Discrete Applied Mathematics》2004,134(1-3):213-237
This paper considers the problem of computing the squared volume of a largest j-dimensional simplex in an arbitrary d-dimensional polytope P given by its vertices (a “V-polytope”), for arbitrary integers j and d with 1⩽j⩽d. The problem was shown by Gritzmann, Klee and Larman to be -hard. This paper examines the possible accuracy of deterministic polynomial-time approximation algorithms for the problem. On the negative side, it is shown that unless , no such algorithm can approximately solve the problem within a factor of less than 1.09. It is also shown that the -hardness and inapproximability continue to hold when the polytope P is restricted to be an affine crosspolytope.On the positive side, a simple deterministic polynomial-time approximation algorithm for the problem is described. The algorithm takes as input integers j and d with 1⩽j⩽d and a V-polytope P of dimension d. It returns a j-simplex S⊂P such thatwhere T is any largest j-simplex in P, and A and B are positive constants independent of j,d,P. 相似文献
2.
The graph G(P) of a polyhedron P has a node corresponding to each vertex of P and two nodes are adjacent in G(P) if and only if the corresponding vertices of P are adjacent on P. We show that if P ? n is a polyhedron, all of whose vertices have (0–1)-valued coordinates, then (i) if G(P) is bipartite, the G(P) is a hypercube; (ii) if G(P) is nonbipartite, then G(P) is hamilton connected. It is shown that if P ? n has (0–1)-valued vertices and is of dimension d (≤n) then there exists a polyhedron P′ ? d having (0–1)-valued vertices such that . Some combinatorial consequences of these results are also discussed. 相似文献
3.
K. Inoue 《Journal of multivariate analysis》1976,6(2):295-308
We consider two Gaussian measures P1 and P2 on (C(G), ) with zero expectations and covariance functions R1(x, y) and R2(x, y) respectively, where Rν(x, y) is the Green's function of the Dirichlet problem for some uniformly strongly elliptic differential operator A(ν) of order , on a bounded domain G in d (ν = 1, 2). It is shown that if the order of A(2) ? A(1) is at most , then P1 and P2 are equivalent, while if the order is greater than , then P1 and P2 are not always equivalent. 相似文献
4.
We study a continuous time growth process on (d?1) associated to the following interacting particle system: initially there is only one simple symmetric continuous time random walk of total jump rate one located at the origin; then, whenever a random walk visits a site still unvisited by any other random walk, it creates a new independent random walk starting from that site. Let us call Pd the law of such a process and S0d(t) the set of sites, visited by all walks by time t. We prove that there exists a bounded, non-empty, convex set , such that for every ε>0, Pd-a.s. eventually in t, the set Sd0(t) is within an ε neighborhood of the set [Cdt], where for we define . Moreover, for d large enough, the set Cd is not a ball under the Euclidean norm. We also show that the empirical density of particles within Sd0(t) converges weakly to a product Poisson measure of parameter one. To cite this article: A.F. Ram??rez, V. Sidoravicius, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 821–826. 相似文献
5.
Alan L.T Paterson 《Journal of Functional Analysis》1983,53(3):203-223
A theory of harmonic analysis on a metric group (G, d) is developed with the model of U, the unitary group of a C1-algebra , in mind. Essential in this development is the set of contractive, irreducible representations of G, and its concomitant set Pd(G) of positive-definite functions. It is shown that is compact and closed in . The set is determined in a number of cases, in particular when G = U() with abelian. If is an AW1-algebra, it is shown that d is essentially the same as . Unitary groups are characterised in terms of a certain Lie algebra u and several characterisations of G = U() when is abelian are given. 相似文献
6.
Václav E. Beneš 《Stochastic Processes and their Applications》1974,2(2):127-140
Girsanov's theorem is a generalization of the Cameron-Martin formula for the derivative of a measure induced by a translation in Wiener space. It states that for ? a nonanticipative Brownian functional with ∫|?|2 ds < ∞ a.s. and with , where , the translated functions are a Wiener process under P?. The Girsanov functionals exp [ζ(?)] have been used in stochastic control theory to define measures corresponding to solutions of stochastic DEs with only measurable control laws entering the right-hand sides. The present aim is to show that these same concepts have direct practical application to final value problems with bounded control. This is done here by an example, the noisy integrator: Make E{x21}∣small, subject to dxt = ut dt + dwt, |u|? 1, xt observed. For each control law there is a definite cost v(1?t, x) of starting at x, t and using that law till t = 1, expressible as an integral with respect to (a suitable) P?. By restricting attention to a dense set of smooth laws, using Itô's lemma, Kac's theorem, and the maximum principle for parabolic equations, it is possible to calculate sgn vx for a critical class of control laws, then to compare control laws, “solve” the Bellman-Hamilton-Jacobi equation, and thus justify selection of the obvious bang-bang law as optimal. 相似文献
7.
R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献
8.
We consider the set of ordered partitions of n into m parts acted upon by the cyclic permutation (12…m). The resulting family of orbits is shown to have cardinality , where φ is Euler's φ-function. is shown to be set-isomorphic to the family of orbits of the set of all m-subsets of an n-set acted upon by the cyclic permutation (12…n). This isomorphism yields an efficient method for determining the complete weight enumerator of any code generated by a circulant matrix. 相似文献
9.
10.
Earl S. Kramer 《Discrete Mathematics》1974,8(2):173-180
A t-design (λ, t, d, n) is a system of sets of size d from an n-set S, such that each t subset of S is contained in exactly λ elements of . A t-design is indecomposable (written IND(λ, t, d, n)) if there does not exist a subset ? such that is a (λ, t, d, n) for some λ, 1 ? λ < λ. A triple system is a (λ; 2, 3, n). Recursive and constructive methods (several due to Hanani) are employed to show that: (1) an IND(2; 2, 3, n) exists for n ≡ 0, 1 (mod 3), n ? 4 and n ≡ 7 (designs of Bhattacharya are used here), (2) an IND(3; 2, 3, n) exists for n odd, n ? 5, (3) if an IND(λ, 2, 3, n) exists, n odd, then there exists an infinite number of indecomposable triple systems with that λ. 相似文献
11.
12.
Let P1,…,Pn be generic homogeneous polynomials in n variables of degrees d1,…,dn respectively. We prove that if ν is an integer satisfying ∑i=1ndi?n+1?min{di}<ν, then all multivariate subresultants associated to the family P1,…,Pn in degree ν are irreducible. We show that the lower bound is sharp. As a byproduct, we get a formula for computing the residual resultant of smooth isolated points in To cite this article: L. Busé, C. D'Andrea, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
13.
Joel Anderson 《Journal of Functional Analysis》1979,31(2):195-217
Three main results are obtained: (1) If is an atomic maximal Abelian subalgebra of (), is the projection of () onto and h is a complex homomorphism on , then h ° is a pure state on (). (2) If {Pn} is a sequence of mutually orthogonal projections with rank(Pn) = n and ∑ Pn = I, is the projection of () onto {Pn}″ given by P(T)=∑tracen(T)Pn and h is a homomorphism on {Pn}″ such that h(Pn) = 0 for all n then h ° induces a type II∞ factor representation of the Calkin algebra. (3) If is a nonatomic maximal Abelian subalgebra of () then there is an atomic maximal Abelian subalgebra of () and a large family {Φα} of 1-homomorphisms from onto such that for each α, Φα ° is an extreme point in the set of projections from () onto . (Here denotes the projection of () onto .) 相似文献
14.
Alan P Sprague 《Journal of Combinatorial Theory, Series B》1978,24(3):294-300
We denote the distance between vertices x and y of a graph by d(x, y), and pij(x, y) = ∥ {z : d(x, z) = i, d(y, z) = j} ∥. The (s, q, d)-projective graph is the graph having the s-dimensional subspaces of a d-dimensional vector space over GF(q) as vertex set, and two vertices x, y adjacent iff . These graphs are regular graphs. Also, there exist integers λ and μ > 4 so that μ is a perfect square, p11(x, y) = λ whenever d(x, y) = 1, and p11(x, y) = μ whenever d(x, y) = 2. The (s, q, d)-projective graphs where and , are characterized by the above conditions together with the property that there exists an integer r satisfying certain inequalities. 相似文献
15.
16.
Curtis Greene 《Journal of Combinatorial Theory, Series A》1976,20(1):69-79
For any partially ordered set P, let denote the cardinality of the largest subset of P obtained by taking the union of k antichains (chains). Then there exists a partition Δ = {Δl ? Δ2 > … ? Δl} of | P | such that dk(P) = Δ1 + Δ2 + … + Δk and for each k, where denotes the partition conjugate to Δ. This result can be used to prove a general class of “Dilworth-type” theorems for subfamilies of P. 相似文献
17.
Michael Klemm 《Journal of Combinatorial Theory, Series A》1984,36(3):364-372
Let d be the minimum distance of an (n, k) code , invariant under an abelian group acting transitively on the basis of the ambient space over a field F with char F × n. Assume that contains the repetition code, that dim( ∏ ⊥) = k ? 1 and that the supports of the minimal weight vectors of form a 2-design. Then d2 ? d + 1 ? n with equality if and only if the design is a projective plane of order d ? 1. The case d2 ? d + 1 = n can often be excluded with Hall's multiplier theorem on projective planes, a theorem which follows easily from the tools developed in this paper Moreover, if d2 ? d + 1 > n and F = GF(2) then (d ? 1)2 ? n. Examples are the generalized quadratic residue codes. 相似文献
18.
David Barnette 《Discrete Mathematics》1974,10(1):9-13
The distance between two vertices of a polytope is the minimum number of edges in a path joining them. The diameter of a polytope is the greatest distance between two vertices of the polytope. We show that if P is a d-dimensional polytope with n facets, then the diameter of P is at most . 相似文献
19.
The main result is the following. Let be a bounded Lipschitz domain in , d?2. Then for every with ∫f=0, there exists a solution of the equation divu=f in , satisfying in addition u=0 on and the estimate where C depends only on . However one cannot choose u depending linearly on f. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 973–976. 相似文献
20.
Steven F Arnold 《Statistics & probability letters》1985,3(5):275-279
Suppose that a statistical decision problem is invariant under a group of transformations g?G. T (X) is equivariant if there exists such that . We show that the minimal sufficient statistic is equivalent and that if T(X) is an equivariant sufficient statistics and d(X) is invariant under G, then is invariant under . 相似文献